Question

Measure the height of the palm tree indirectly using a mirror that is placed on the ground a certain distance away from the tree. The distance from the

mirror to the base of the palm tree is 2.5 m and the distance from the mirror to the person's foot is 0.5 m. The person is 1.78 m tall.

Answer 1

(b) 8.9 m

Explanation:

The mirror ensures that angle 1 is congruent to angle 2, so the triangles in the diagram are similar. The ratios of height to mirror distance are proportional.

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setup

The height of the object is proportional to its distance from the mirror, so we have ...

(tree height)/(tree-to-mirror) = (person height)/(person-to-mirror)

(tree height)/(2.5 m) = (1.78 m)/(0.5 m)

solution

Multiplying this proportion by 2.5 m, we find ...

tree height = (2.5 m)(1.78/0.5) = 8.9 m

The height of the palm tree is 8.9 meters.